In this work, we analyze the simulation of frictional contact
mechanics coupled with the fluid flow in a fracture network and present a scalable and efficient
preconditioning framework for the linear system arising from the discretization and linearization of
the coupled problem. As to the discretization approach, we elect to use the Discrete Fracture Model
(DFM) [1]}, i.e., an explicit representation of the fracture surfaces, while
the constraints are imposed with the aid of Lagrange multipliers [2]}, [3]}, [4]}, [5]}, [6]}. As it is common in geological and
reservoir simulations, we rely on low-order finite elements for the mechanics and
a cell-centered finite volume scheme for the fluid flow. Lagrange multipliers are the contact forces acting on
the fracture surfaces as a cell-centered variable, thus sharing the same representation as the fluid
pressure field with no interpolation needed. The details of this
discretization scheme are described in [7]}. This approach is unstable in the
Ladyzhenskaya-Babuška-Brezzi
(LBB) sense, i.e., it does not uniformly satisfy the
inf-sup condition [8]}, and
requires a stabilization. In this work, we use the
global algebraic approach introduced in the reference work [7]}. The Jacobian matrix arising
from the described problem is non-symmetric with a \(3 \times 3\)  block structure, which has to be properly preconditioned to allow for a robust, scalable and efficient solution with the aid of Krylov subspace solvers.
